A Weyl-Titchmarsh type formula for a discrete Schrödinger operator with Wigner-von Neumann potential. (English) Zbl 1205.47029

Janas, Jan; Simonov, Sergey

Stud. Math. 201, No. 2, 167-189 (2010).

Summary: We consider a discrete Schrödinger operator \(\mathcal J\) with Wigner-von Neumann potential not belonging to \(l^2\). We find the asymptotics of orthonormal polynomials associated to \({\mathcal J}\). We prove a Weyl-Titchmarsh type formula, which relates the spectral density of \({\mathcal J}\) to a coefficient in the asymptotics of the orthonormal polynomials.

MSC:

47B36	Jacobi (tridiagonal) operators (matrices) and generalizations
34E10	Perturbations, asymptotics of solutions to ordinary differential equations